Question

The difference of two number is five sixth of their sum and the greater exceeds ten times the lesser by $3$.find the numbers.

Answer 1

Let the two numbers be $x$ and $y.$

According to the question ,

$x-y=\frac{5}{6}(x+y)\Rightarrow 6(x-y)=5(x+y)\Rightarrow 6x-6y=5x+5yx-11y=0⟶\left(i\right)$

Also$,x-10y=3⟶\left(ii\right)$

So ,

$x-11y=0x-10y=3$

On substraction : $-y=-3$

$y=3$

putting the value of $y$ in equation $⟶\left(i\right)$

$x-11\left(3\right)=0x=33$